Divergent series, summability and resurgence.: III, Resurgent methods and the first Painlevé equation
(Web Content)
Author:
Series:
Lecture notes in mathematics (Springer-Verlag) ; volume 2155.
Published:
Switzerland : Springer, 2016.
Format:
Web Content
Content Description:
1 online resource (xxii, 230 pages) : illustrations (some color).
Status:
Available Online
Description
The aim of this volume is two-fold. First, to show how the resurgent methods introduced in volume 1 can be applied efficiently in a non-linear setting; to this end further properties of the resurgence theory must be developed. Second, to analyze the fundamental example of the First Painlevé equation. The resurgent analysis of singularities is pushed all the way up to the so-called "bridge equation", which concentrates all information about the non-linear Stokes phenomenon at infinity of the First Painlevé equation. The third in a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists who are interested in divergent power series and related problems, such as the Stokes phenomenon. The prerequisites are a working knowledge of complex analysis at the first-year graduate level and of the theory of resurgence, as presented in volume 1.
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Language:
Unknown
ISBN:
9783319290003, 3319290002
UPC:
10.1007/978-3-319-29000-3
Notes
Bibliography
Includes bibliographical references and index.
Description
The aim of this volume is two-fold. First, to show how the resurgent methods introduced in volume 1 can be applied efficiently in a non-linear setting; to this end further properties of the resurgence theory must be developed. Second, to analyze the fundamental example of the First Painlevé equation. The resurgent analysis of singularities is pushed all the way up to the so-called "bridge equation", which concentrates all information about the non-linear Stokes phenomenon at infinity of the First Painlevé equation. The third in a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists who are interested in divergent power series and related problems, such as the Stokes phenomenon. The prerequisites are a working knowledge of complex analysis at the first-year graduate level and of the theory of resurgence, as presented in volume 1.
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Citations
APA Citation (style guide)
Delabaere, Ã. (2016). Divergent series, summability and resurgence. Springer.
Chicago / Turabian - Author Date Citation (style guide)Delabaere, Éric. 2016. Divergent Series, Summability and Resurgence. Springer.
Chicago / Turabian - Humanities Citation (style guide)Delabaere, Éric, Divergent Series, Summability and Resurgence. Springer, 2016.
MLA Citation (style guide)Delabaere, Éric. Divergent Series, Summability and Resurgence. Springer, 2016.
Note! Citation formats are based on standards as of July 2022. Citations contain only title, author, edition, publisher, and year published. Citations should be used as a guideline and should be double checked for accuracy.
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Grouped Work ID:
08698915-2dc0-182f-33b1-e18d8a009936
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Record Information
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| 100 | 1 | |a Delabaere, Éric, |0 https://id.loc.gov/authorities/names/no2007107743 |e author. | |
| 245 | 1 | 0 | |a Divergent series, summability and resurgence. |n III, |p Resurgent methods and the first Painlevé equation / |c Eric Delabaere. |
| 246 | 3 | 0 | |a Resurgent methods and the first Painlevé equation |
| 264 | 1 | |a Switzerland : |b Springer, |c 2016. | |
| 300 | |a 1 online resource (xxii, 230 pages) : |b illustrations (some color). | ||
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| 490 | 1 | |a Lecture notes in mathematics, |x 0075-8434 ; |v 2155 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |6 880-01 |a Avant-Propos -- Preface to the three volumes -- Preface to this volume -- Some elements about ordinary differential equations -- The first Painlevé equation -- Tritruncated solutions for the first Painlevé equation -- A step beyond Borel-Laplace summability -- Transseries and formal integral for the first Painlevé equation -- Truncated solutions for the first Painlevé equation -- Supplements to resurgence theory -- Resurgent structure for the first Painlevé equation -- Index. | |
| 520 | |a The aim of this volume is two-fold. First, to show how the resurgent methods introduced in volume 1 can be applied efficiently in a non-linear setting; to this end further properties of the resurgence theory must be developed. Second, to analyze the fundamental example of the First Painlevé equation. The resurgent analysis of singularities is pushed all the way up to the so-called "bridge equation", which concentrates all information about the non-linear Stokes phenomenon at infinity of the First Painlevé equation. The third in a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists who are interested in divergent power series and related problems, such as the Stokes phenomenon. The prerequisites are a working knowledge of complex analysis at the first-year graduate level and of the theory of resurgence, as presented in volume 1. | ||
| 588 | 0 | |a Online resource; title from PDF title page (SpringerLink, viewed July 8, 2016). | |
| 650 | 0 | |a Divergent series. |0 https://id.loc.gov/authorities/subjects/sh85120240 | |
| 650 | 0 | |a Summability theory. |0 https://id.loc.gov/authorities/subjects/sh85130426 | |
| 650 | 0 | |a Painlevé equations. |0 https://id.loc.gov/authorities/subjects/sh86005937 | |
| 650 | 6 | |a Séries divergentes. | |
| 650 | 6 | |a Sommabilité. | |
| 650 | 6 | |a Équations de Painlevé. | |
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| 650 | 7 | |a Divergent series. |2 fast | |
| 650 | 7 | |a Painlevé equations. |2 fast | |
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| 776 | 0 | 8 | |i Print version: |a Delabaere, Éric. |t Divergent series, summability and resurgence. III, Resurgent methods and the first Painlevé equation. |d Switzerland : Springer, 2016 |z 3319289993 |z 9783319289991 |w (OCoLC)932096104 |
| 830 | 0 | |a Lecture notes in mathematics (Springer-Verlag) ; |0 https://id.loc.gov/authorities/names/n42015165 |v 2155. |x 0075-8434 | |
| 880 | 8 | |6 505-01/(S |a 4.2.2.2 The Riemann Surface RZ, ζ0 | |
| 880 | 8 | |6 505-00/(S |a 3.4 First Painlevé Equation and Tritruncated Solutions3.4.1 Reminder; 3.4.2 Formal Series Solution and Borel-Laplace Summation; 3.4.2.1 Borel-Laplace Summation; 3.4.2.2 A Link with 1-summability Theory; 3.4.2.3 Miscellaneous Properties; 3.4.2.4 Asymptotics and Approximations; 3.4.3 Tritruncated Solutions; 3.4.3.1 Tritruncated Solutions; Exercices; References; Chapter 4 A Step Beyond Borel-Laplace Summability; 4.1 Introduction; 4.2 Resurgent Functions and Riemann Surface; 4.2.1 Notation; 4.2.2 The Riemann Surface of Z-Resurgent Functions; 4.2.2.1 The Space RZ, ζ0 | |
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